Apparatus for displaying images to viewers in motion

ABSTRACT

Apparatus for displaying still images to viewers in motion relative to those images, such as passengers on a subway train, includes a plurality of images mounted on a surface, and a slitboard mounted between that surface and the viewer. As the viewers pass by, the slitboard acts like a shutter, creating an animation effect. In addition, there is a stretching or widening effect that enlarges the images, allowing images to be &#34;preshrunk,&#34; thereby allowing a large number of images in a small space, increasing the available frame rate of the animation. The stretching effect depends on the distance between the image surface and the slitboard.

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This is a continuation of co-pending, commonly assigned U.S.patent application Ser. No. 10/424,239, filed Apr. 25, 2003, now U.S.Pat. No. ______, which is a division of U.S. patent application Ser. No.09/362,767, filed Jul. 28, 1999, now U.S. Pat. No. 6,564,486, whichclaims the benefit of U.S. Provisional Patent Applications Nos.60/094,484, 60/127,164, and 60/134,747, filed Jul. 29, 1998, Mar. 26,1999, and May 18, 1999, respectively.

BACKGROUND OF THE INVENTION

[0002] This invention relates to the display of still images that appearanimated to a viewer in motion relative to the still images. Moreparticularly, this invention relates to the display of such still imagesin spatially-constrained environments.

[0003] Display devices that display still images appearing to beanimated to a viewer in motion are known. These devices include a seriesof graduated images (i.e., adjacent images that differ slightly andprogressively from one to the next). The images are arranged in thedirection of motion of a viewer (e.g., along a railroad) such that theimages are viewed consecutively. As a viewer moves past these images,they appear animated. The effect is similar to that of a flip-book. Aflip-book has an image on each page that differs slightly from the onebefore it and the one after it such that when the pages are flipped, aviewer perceives animation.

[0004] A longstanding trend in mass transportation systems has been thedevelopment of installations to provide the passengers in subway systemswith animated motion pictures. The animation of these motion pictures iseffected by the motion of the viewer relative to the installation, whichis fixed to the tunnel walls of the subway system. Such installationshave obvious value: the moving picture is viewable through the trainwindows, through which only darkness would otherwise be visible.Possible useful moving picture subjects could be selections of artisticvalue, or informative messages from the transportation system or from anadvertiser.

[0005] Each of the known arrangements provides for the presentation of aseries of graduated images, or “frames,” to the viewer/rider so thatconsecutive frames are viewed one after the other. As is well known, thesimple presentation of a series of still images to a moving viewer isperceived as nothing more than a blur if displayed too close to theviewer at a fast rate. Alternatively, at a large distance or low speeds,the viewer sees a series of individual images with no animation. Inorder to achieve a motion picture effect, known arrangements haveintroduced methods of displaying each image for extremely short periodsof time. With display times of sufficiently short duration, the relativemotion between viewer and image is effectively arrested, and blurring isnegligible. Methods for arresting the motion have been based onstroboscopic illumination of the images. These methods require precisesynchronization between the viewer and the installation in order thateach image is illuminated at the same position relative to the viewer,even as the viewer moves at high speed.

[0006] The requirements of a stroboscopic device are numerous: the flashmust be extremely brief for a fast moving viewer, and thereforecorrespondingly bright in order that enough light reach the viewer. Thisrequirement, in turn, requires extremely precisely timed flashes. Thisprecision requires extremely consistent motion on the part of theviewer, with little or no change in speed. All of the aforementionedrequirements result in a high level of mechanical or electricalcomplexity and cost, or greater consistency in train motion than exists.Other known arrangements have overcome the need for high temporalprecision by providing a transponder of some sort on the viewer'svehicle and a receiver on the installation to determine the viewer'sposition. These arrangements involve considerable mechanical andelectrical complexity and cost.

[0007] The aforementioned known arrangements generally require theviewer to be in a vehicle. This requirement may be imposed because thevehicle carries equipment for timing, lighting, or signaling; or becauseof the need to maintain high consistency in speed; or to increase theviewer's speed, for example. The use of a vehicle requires a high levelof complexity of the design because of the number of mechanical elementsand because one frequently is dealing with existing systems, requiringmodification of existing equipment. The harsh environment of beingmounted on a moving subway car may limit the mechanical or electricalprecision attainable in any unit that requires it, or it may requirefrequent maintenance for a part where high precision has been attained.

[0008] The use of a vehicle also imposes constraints. At the most basiclevel, it limits the range of possible applications to those whereviewers are on vehicles. More specifically, considerations of thevehicle's physical dimensions constrain a stroboscopic device'sapplicability. The design must take into account such information as thevehicle's height and width, its window size and spacing, and thepositions of viewers within the vehicle. For example, close spacing ofwindows on a high speed train requires that stroboscopic dischargespreferably be of high frequency and number in order that the display bevisible to all occupants of a train. The dimensions of the environment,such as the physical space available for hardware installation in thesubway tunnel and the distances available over which to project images,impose further constraints on the size of elements of any device as wellas on the quality and durability of its various parts.

[0009] Though in principle a stroboscopic device can work for slowlymoving viewers, simply by spacing the projectors more closely, inpractice it is difficult. First, closer spacing increases cost andcomplexity. Also, once the device is installed with a fixedprojector-to-projector distance, a minimum speed is imposed on theviewer.

[0010] An existing method for the display of animated images involvingrelative motion between the viewer and the device is the zootrope. Thezootrope is a simple hollow cylindrical device that produces animationby way of the geometrical arrangement of slits cut in the cylinder wallsand a series of graduated images placed on the inside of the cylinder,one per slit. When the cylinder is spun on its axis, the animation isvisible through the (now quickly moving) slits.

[0011] The zootrope is, however, fixed in nearly all its proportionsbecause its cross section must be circular. Since the animation requiresa minimum frame rate, and the frame rate depends on the rotationalspeed, only a very short animation can be viewed using a zootrope.Although there is relative motion between the viewer and the apparatus,in practice the viewer cannot comfortably move in a circle around thezootrope. Therefore only one configuration is practicable with azootrope: that in which a stationary viewer observes a short animationthrough a rotating cylinder.

[0012] For the reasons of its incapacity to be altered in shape, theshort duration of its animation, and the fact that it must be spun, thezootrope has remained a toy or curiosity without practical application.However, at least one known system displays images along an outdoorrailroad track in an arrangement that might be referred to as a “linearzootrope” in which the images are mounted behind a wall in which slitsare provided. That outdoor environment is essentially unconstrained.

[0013] In view of the foregoing, it would be desirable to be able toprovide apparatus for use in a spatially-constrained environment thatdisplays still images that appear animated to a viewer in motion.

[0014] It would also be desirable to be able to provide such apparatusfor use in a spatially-constrained environment having low ambientlighting levels.

SUMMARY OF THE INVENTION

[0015] It is an object of this invention to attempt to provide apparatusfor use in a spatially-constrained environment that displays stillimages that appear animated to a viewer in motion.

[0016] It is also an object of this invention to attempt to provide suchapparatus for use in a spatially-constrained environment having lowambient lighting levels.

[0017] In accordance with this invention, there is provided apparatusfor displaying a plurality of still images, forming an animated display,to a viewer moving substantially at a known velocity relative to saidstill images substantially along a known trajectory substantiallyparallel to said still images. The apparatus includes a backboard havinga backboard length along the trajectory. The still images are mounted ona surface of the backboard, with each of said still images having anactual image width and having an image center. Image centers of adjacentimages are separated by a frame-to-frame distance. A slitboard ispositioned substantially parallel to the backboard, facing said surfacethereof and separated therefrom by a board-to-board distance. Theslitboard is mounted at a viewing distance from the trajectory. Theboard-to-board distance and the viewing distance total a backboarddistance. The slitboard has a slitboard length along the trajectory, andhas a plurality of slits substantially perpendicular to the slitboardlength. Each slit corresponds to one of the images and has a slit widthmeasured along the slitboard length and a slit center, respective slitcenters of adjacent ones of the slits being separated by theframe-to-frame distance. In order to display each image with an apparentimage width, the board-to-board distance, the viewing distance and theactual image width are selected so that the product of (a) the actualimage width and (b) the quotient of (i) the viewing distance and (ii)the board-to-board distance substantially equals the apparent imagewidth. In order to project each image substantially without blurring,the slit width is selected to be at most about one-tenth of the actualimage width.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The above and other objects and advantages of the invention willbe apparent upon consideration of the following detailed description,taken in conjunction with the accompanying drawings, in which likereference characters refer to like parts throughout, and in which:

[0019]FIG. 1 is a perspective view of a preferred embodiment ofapparatus according to the present invention;

[0020]FIG. 2 is an exploded perspective view of the apparatus of FIG. 1;

[0021]FIG. 2A is a perspective view of an alternative preferredembodiment of the apparatus of FIGS. 1 and 2;

[0022]FIG. 3 is a schematic diagram of the geometry and optics of theapparatus of FIGS. 1 and 2;

[0023]FIG. 3A is a schematic diagram of the geometry of a curvedembodiment of the invention;

[0024]FIGS. 4A, 4B and 4C (collectively “FIG. 4”) are schematicrepresentations of a single image and slit with a viewer at threedifferent positions at three different instants of time;

[0025]FIGS. 5A, 5B and 5C (collectively “FIG. 51”) are schematicrepresentations of a pair of images and slits with a viewer at threedifferent positions at three different instants of time;

[0026]FIG. 6 is a schematic representation of a single image beingviewed by a viewer over time, illustrating the stretching effect;

[0027]FIG. 6A is a schematic representation illustrating the stretchingeffect where the backboard is not parallel to the direction of motion;

[0028]FIG. 7 is a schematic plan view of a second preferred embodimentof the invention wherein the images are curved;

[0029]FIG. 8 is a schematic plan view of a third preferred embodiment ofthe invention wherein the images are inclined relative to the backboard;

[0030]FIG. 9 is a schematic plan view of a fourth preferred embodimentof the invention, similar to the embodiment of FIG. 8, but wherein theslitboard includes a series of sections parallel to the images andinclined relative to the backboard;

[0031]FIG. 10 is a schematic perspective representation of a pair ofcombination slitboard/backboards from a fifth preferred embodiment ofthe invention which is two-sided;

[0032]FIG. 11 is a schematic plan view of the embodiment of FIG. 10;

[0033]FIG. 12 is a schematic plan view of a sixth embodiment havingcurved images such as in the embodiment of FIG. 7, and being two-sidedsuch as in the embodiment of FIGS. 10 and 11;

[0034]FIG. 13 is a perspective view of a roller-type image holder foruse in a seventh preferred embodiment of the invention;

[0035]FIG. 14 is a perspective view of an eighth preferred embodiment ofthe invention;

[0036]FIG. 15 is a vertical cross-sectional view, taken from line 15-15of FIG. 14, of the eighth preferred embodiment of the invention; and

[0037]FIG. 16 is a simplified perspective view showing the mounting of aplurality of modular units according the invention in a subway tunnel.

DETAILED DESCRIPTION OF THE INVENTION

[0038] It is the purpose of the present invention to produce a simpleapparatus operating on principles of simple geometric optics thatdisplays animation to a viewer in motion relative to it. The apparatusrequires substantially only that the viewer move in a substantiallypredictable path at a substantially predictable speed. There are manycommon instances that meet this criterion, including, but not limitedto, riders on subway trains, pedestrian on walkways or sidewalks,passengers on surface trains, passengers in motor vehicles, passengersin elevators, and so on. For the remainder of this document, for ease ofdescription, reference will primarily be made to a particular exemplaryapplication—an installation in a subway system, viewable by the riderson a subway train—but the present invention is not limited to such anapplication.

[0039] Benefits of the present invention include the following:

[0040] 1. It preferably does not require that the viewer be in avehicle.

[0041] 2. It preferably obviates the need for complex stroboscopicillumination.

[0042] 3. It preferably obviates the need for precise timing orpositioning triggers between the apparatus and the viewer.

[0043] 4. It preferably obviates the need for moving parts.

[0044] 5. It preferably requires no shutter.

[0045] 6. It preferably requires no special equipment to be mounted onthe viewer or the viewer's vehicle, if the viewer is on a vehicle.

[0046] 7. It preferably requires no transfer of information between theapparatus and the viewer pertaining to the viewer's position, speed ordirection of motion.

[0047] 8. It preferably offers very high depth of field of viewability.

[0048] 9. It preferably operates as designed independently of thedirection of the viewer's motion.

[0049] 10. It preferably is effective for each member of a closelyspaced series of viewers, independent of their spacing or relativemotions.

[0050] 11. It preferably requires no optics more precise than a simpleslit (although other optics may be used).

[0051] 12. It preferably requires no correlation between vehicle windowspacing and picture spacing.

[0052] 13. It preferably offers the possibility of effectivemagnification of the image in the direction of motion.

[0053] 14. It preferably requires very low minimum viewer speed due tothe fact that the magnification allows very close spacing of graduatedimages.

[0054] 15. It preferably does not require a particular geometry, be itcircular, linear, or any other geometry.

[0055] 16. It preferably has no maximum speed.

[0056] The apparatus preferably includes a series of graduated pictures(“images” or “frames”) spaced at preferably regular intervals and,preferably between the pictures and the viewer, an optical arrangementthat preferably restricts the viewer's view to a thin strip of eachpicture. This optical arrangement preferably is an opaque material witha series of thin, transparent slits in it—one slit per picture—orientedwith the long dimension of the slit perpendicular to the direction ofthe viewer's motion. The series of pictures will generally be called a“backboard” and the preferred optical arrangement will generally becalled a “slitboard.”

[0057] Not essential to the invention, but often desirable, is a sourceof illumination so that the pictures are brighter than the viewer'senvironment. The illumination can back-light the pictures or can beplaced between the slitboard and backboard to front-light the picturessubstantially without illuminating the viewer's environment. Whenlighting is used it preferably should be constant in brightness. Naturalor ambient light can be used. If ambient light is sufficient, theapparatus can be operated without any built-in source of illumination.

[0058] Also not necessary, but often desirable, is to make the viewerside of the slitboard dark or nonreflecting, or both, in order tomaximize the contrast between the pictures viewable through theslitboard and the slitboard itself. However, the slitboard need notnecessarily be dark or nonreflective. For example, the viewer face ofthe slitboard could have a conventional billboard placed on it withslits cut at the desired positions. This configuration is particularlyuseful in places where some viewers are moving relative to the deviceand others are stationary. This may occur, for example, at a subwaystation where an express train passes through without stopping, butpassengers waiting for a local train stand on the platform. The movingviewers preferably will see the animation through the imperceptible blurof the conventional billboard on the slitboard front. The stationaryviewers preferably will see only the conventional billboard.

[0059] The invention will now be described with reference to FIGS. 1-16.

[0060] The basic construction of a preferred embodiment of a displayapparatus 10 according to the present invention is shown in FIGS. 1 and2. In this embodiment, apparatus 10 is essentially a rectangular solidformed by housing 20 and lid 21. The front and rear of apparatus 10preferably are formed by slitboard 22 and backboard 23, which aredescribed in more detail below. Slitboard 22 and backboard 23 preferablyfit into slots 24 in housing 20 which are provided for that purpose.Lightframe 25 preferably is interposed between housing 20 and lid 21 andpreferably encloses light source 26, which preferably includes twofluorescent tubes 27, to light images, or “frames” 230, on backboard 23.Slitboard 22 preferably includes a plurality of slits 220 as describedin more detail below. Preferably, in order to keep foreign matter out ofapparatus 10, particularly if it is to be used in a harsh or dirtyenvironment such as a subway tunnel, each slit 220 is covered by alight-transmissive, preferably transparent cover 221 (only one shown).Alternatively, each slit 220 may be covered by a semicylindrical lens222 (only one shown), which also improves the resolution of viewedimages. Specifically, if the focal length of the lens is approximatelyequal to the distance between slitboard 22 and backboard 23, theresolution of the image may be increased. This improvement of theresolution is effected by narrowing the width of the sliver of theactual image visible at a given instant by the viewer. Alternatively,the use of lenses may allow the slit width to be increased withoutlowering resolution.

[0061] In an alternative embodiment 200, shown in FIG. 2A, housing 201is similar to housing 20, except that it includes light-transmissive,preferably transparent, front and rear walls 202, 203 respectively,forming a completely enclosed structure. At least one of walls 202, 203(as shown, it is wall 202) preferably is hinged as at 204 to form amaintenance door 205 which may be opened, e.g., to replace backboard 23(to change the images 230 thereon) or to change light bulbs 27). Asshown in FIG. 2A, light bulbs 27 are provided in a backlight unit 206instead of lightframe 25, necessitating that backboard 23 and images 230be light-transmissive. Of course, embodiment 200 could be used withlightframe 25 instead of backlight unit 206. Similarly, apparatus 10could be provided with backlight unit 206 instead of lightframe 25, inwhich case backboard 23 and images 230 would be light-transmissive.

[0062]FIG. 3 is a schematic plan view of a portion of apparatus 10 beingobserved by a viewer 30 moving at a substantially constant velocityV_(w) along a track 31 substantially parallel to apparatus 10. Track 31is drawn as a schematic representation of a railroad track, but may beany known trajectory such as a highway, or a walkway or sidewalk, onwhich viewers move substantially at a known substantially constantvelocity.

[0063] The following variables may be defined from FIG. 3:

[0064] D_(s)=slit width

[0065] D_(ff)=frame-to-frame distance

[0066] D_(bs)=backboard-to-slitboard distance

[0067] V_(w)=speed of viewer relative to apparatus

[0068] D_(sb)=thickness of slitboard

[0069] D_(i)=actual width of a single image frame

[0070] D_(vs)=distance from viewer to slitboard

[0071] Other parameters, which are not labeled, will be described below,including B (brightness), c (contrast), and D_(i′) (apparent orperceived width of a single image frame).

[0072] An alternative geometry is shown in FIG. 3A, where track 31′ iscurved, and slitboard 22′ and backboard 23′ are correspondingly curved,so that all three are substantially “parallel” to one another. Althoughnot labeled in FIG. 3A, the other parameters are the same as in FIG. 3,except that, depending on the degree of curvature, there may be someadjustment in the amount of stretching or enlargement of the image asdiscussed below.

[0073] One of the most significant departures of the present inventionfrom previously known apparatus designed to be viewed from a movingvehicle is that no attempt is made to arrest the apparent motion of theimage. That is, in the present device the image is always in motionrelative to the viewer, and some part of the image is always viewable bythe viewer. This contrasts with known systems for moving viewers where astroboscopic flash is designed to be as close as instantaneous aspossible in order to achieve an apparent cessation of motion of anindividual image frame, despite its true motion relative to the viewer.

[0074] As with all animation, the apparatus according to the inventionrelies on the well known effect of persistence of vision, whereby aviewer perceives a continuous moving image when shown a series ofdiscrete images. The operation of the invention uses two distinct, butsimultaneous, manifestations of persistence of vision. The first occursin the eye reconstructing a full coherent image, apparently entirelyvisible at once, when actually shown a small sliver of the image thatsweeps over the whole image. The second is the usual effect of theflip-book, whereby a series of graduated images is perceived to be acontinuous animation.

[0075]FIG. 4 illustrates the first persistence of vision effect. Itshows the position of viewer 30 relative to one image at successivepoints (FIGS. 4A, 4B, 4C) in time. In each of FIGS. 4A, 4B and 4C,double-ended arrow 40 represents the total actual image width, D_(i),while distance 41 represents the portion of the image visible at a giventime. This diagram shows that viewer 30, over a short period of time,gets to see each part of the image. However, at any given instant only athin sliver of the picture, of width 41, is visible. Because the periodof time over which the sliver is visible is very short, and thereforethe motion of the image viewed through the slit in that time is verysmall, the viewer perceives very little or no blur, even at very highspeeds. There is no theoretical upper limit on the speed at which theapparatus works—the faster the viewer moves, the less time a givensliver is visible. That is, the effect that would cause blur—theviewer's increased speed—is cancelled by effect that reduces blur—theperiod of viewability of a given sliver.

[0076] In FIG. 4 the representation of movement of the viewer's eye ispurely illustrative. In practice the viewer's gaze is fixed at a screenthat is perceived to be stationary, and the entirety of the frame can beseen through peripheral vision, as with a conventional billboard.

[0077]FIG. 5 illustrates the second persistence of vision effect. Itshows viewer 30 looking in a fixed direction at three successive pointsin time. In FIG. 5A, a thin sliver of a first image n is in the directline of the viewer's gaze through slit 221. In FIG. 5B, the viewer'sdirect gaze falls on a blocking part of slitboard 22. For the durationthat the opaque part of slitboard 22 is in the line of the viewer'sdirect gaze, the viewer continues to perceive the sliver of image n justseen through slit 221. In FIG. 5C, the direct line of the viewer's gazefalls on slit 222, adjacent to slit 221, and viewer 30 sees a sliver ofadjacent image n+1. Because each slit 221, 222 preferably issubstantially perfectly aligned with its respective image, the sliversvisible at a given angle in the two separate slots preferably correspondsubstantially precisely. That is, at a position, say, three inches fromthe left edge of the picture, the sliver three inches from the left edgeof the picture is viewable from one frame to the next, and never asliver from any other part of the image. In this way, the alignmentbetween the slit and the image prevents the confusion and blur perceivedby the viewer that otherwise would be caused by the fast motion of theimages. Because successive frames differ slightly as with successiveimages in conventional animations, the viewer perceives animation.

[0078] The two persistence of vision effects operate simultaneously inpractice. Above a minimum threshold speed, viewer 30 perceives neitherdiscrete images nor discrete slivers.

[0079] A very useful effect of apparatus 10 is the apparent stretching,or widening, of the image in the direction of motion. FIG. 6 illustratesthe geometrical considerations explaining this stretching effect.Labeled “Position 1” and “Position 2” are the two positions of a givenframe 230 where the opposite edges of frame 230 are visible. Because thepositions of frame 230 and slit 220 are fixed relative to each other,they precisely determine the angle at which viewer 30 must look in orderthat slit 220 be aligned with an edge of the image 230.

[0080] At Position 1, the left edge of image 230 is aligned with slit220 and the viewer's eye. At Position 2, the right edge of image 230 isaligned with slit 220 and the viewer's eye. In fact, the two positionsoccur at different times, but, as explained above, this is not observedby the viewer 30. Only one full image is observed.

[0081] If x is the distance from the centerpoint between the twopositions of slit 220 to either of the individual positions at Position1 or Position 2, then the perceived width of the image, D_(i′), is 2x.By similar triangles,

D _(vs) /X=(D _(vs) +D _(bs))/(x+D _(i)/2)

x(D _(vs) +D _(bs))=(x+D _(i)/2)D _(vs)

2x=(D _(vs) /D _(bs))D _(i)

D _(i′)=(D _(vs) /D _(bs))D _(i)  (1)

[0082] Thus the perceived width of the image, D_(i′), is increased overthe actual width of the image by a factor of the ratio of theviewer-slitboard distance to the slitboard-backboard distance.

[0083]FIG. 6A shows the magnification effect when the backboard 231 isnot substantially parallel to the viewer's trajectory. The magnificationis found by defining a formula f(x), where x is the distance along theviewer's trajectory, for the shape of the backboard—that is, thedistance of the backboard from the axis defined by the viewer'strajectory—around each slit (for example, FIG. 7 shows a backboard 71 onwhich each image 730 forms a semicircle around its respective slit 220).For ease of convention, one can define an x axis along the direction ofthe viewer's motion and a y axis perpendicular to the x axis and choosethe origin at the position of the viewer 30.

[0084] To find the magnification, one determines how an arbitrarypicture element 2301 on the backboard 23′ will appear to viewer 30 on aprojected flat backboard 23″. In FIG. 6A, a section of the truebackboard 23′ is shown between slitboard 22 and the projected backboard23″. A length PR of the backboard 23′ defines a picture element 230′.This section 230′ will appear to viewer 30 as if on projected flatbackboard 23″, as indicated.

[0085] For ease of presentation, the section of backboard 23′ shown is astraight line segment, but this linearity is not required. Also, thebackboard shape does not need to be perfectly described by a formulay=f(x). In practice one can approximate the backboard's true shape in anumber of ways—for example, by treating the backboard as a series ofinfinitesimal elements, each of which can be approximated by a linesegment.

[0086] Viewer 30, at position A, sees the left edge P of picture element230′ when slit 220 is at Q. Because the positions of picture element230′ and slit 220 are fixed relative to each other, they preciselydetermine the angle at which viewer 30 must look in order that slit 220be aligned with an edge of the element 230′. Therefore, the right edge Rof this picture element 230′ will be visible when the device has movedrelative to viewer 30 to a position where a line parallel to QR passesthrough A.

[0087] The left edge of picture element 230′ will appear on projectedbackboard 23″ at position B, a distance Ax from the y axis. The rightedge of picture element 230′ will appear on projected backboard 23″ atposition C. The apparent width of the image, D_(i′), is the distance BC.

[0088] Point P is the intersection of backboard 23′ with the linethrough A and B.

[0089] Point Q is the intersection of slitboard 22 with the line throughA and B.

[0090] Point R is the intersection of backboard 23′ with the linethrough Q and R.

[0091] The distance D_(i) is the distance from P to R.

[0092] The coordinates of the point P, (P_(x),P_(y)), are the solution(x,y) to y=f(x) and

y=(D _(vb) /Δx)x,  (A)

[0093] where the latter equation is the formula for the line through Aand B.

[0094] The coordinates of point Q, (Q_(x), Q_(y)), are the solution(x,y) to y=(D_(vb)/ΔX)x, and

y=D_(bs.)  (B)

[0095] The coordinates of point R, (R_(x),R_(y)), are the solution (x,y)to y=f(x) and

y−Q _(y)=((Δx+D _(i′))/D _(vb))(x−Q _(x)).  (C)

[0096] Finally, the size D_(i) that picture element 230′ should have inorder that it stretch to size D_(i′) is given by

D _(i)=((R _(x) −P _(x))²+(R _(y) −P _(y))²)^(0.5),  (D)

[0097] where the variables on the right hand side can all be found interms of dimensions of the apparatus and Δx.

[0098] The above derivations demonstrate practical methods fordetermining the stretching effect in order to preshrink an image foreither substantially parallel or nonparallel backboards. A useful ruleof thumb which is true for either backboard configuration comes from thefact that angle BAC is equal to angle BQC—the angular size of theprojected image as seen by the viewer is the same as the angular size ofthe actual image at the position of slit 220.

[0099] In order to preshrink an image, it can be divided into manyelements, starting at Δx=0 and moving sequentially in either directionwhile incrementing Δx appropriately. Then each element can be preshrunkand placed at the appropriate location on the backboard.

[0100] In cases where the viewer's trajectory is curved, such as thegeometry shown in FIG. 3A, neither the slitboard nor the backboard willnecessarily be a straight line. A similar derivation can be used to theone for nonparallel backboards, by defining an function g(x) for thepath of the slit relative to the viewer and replacing Relation (B) withy=g(x).

[0101] In practice, the images may be shrunk in the direction of motionbefore being mounted on the backboard in order that when projected theyare stretched to their proper proportions, allowing a large image to bepresented in a relatively smaller space. Curved or inclined surfaces onthe backboard can be used to augment the effect. That is, as anon-planar backboard approaches the slitboard, the magnificationincreases greatly. However, for simplicity, the discussion that followswill assume a planar backboard unless otherwise indicated.

[0102] As shown below, the stretching effect, when adjusted through therelevant variable parameters of apparatus 10, can be very useful. Also,the relation between the perceived image size, D_(i′), and the viewerdistance, D_(vs), is linear—the image gets bigger as the viewer movesfarther away. This can be a useful effect in the right environment.

[0103] There are some limitations and side effects. Both effects ofpersistence of vision require minimum speeds that are not necessarilyequal. Too slow a speed can result in the appearance of only discretevertical lines, or flicker, or a lack of observed animation effect. Inpractice, the appearance of only discrete vertical lines is the dominantlimitation. A possibly useful effect of the stretching effect arisesfrom the fact that slivers of multiple frames are visible at the sametime. That is, if the perceived image is ten times larger than the trueimage, slivers of ten different images may be visible at any given time.Because each frame presents a different point in time in the animation,multiple times of the image may be simultaneously viewable. This effectmay, for example, be used to interlace images, if desired. Similarly,multiple instances of a single frame can be displayed, in a mannersimilar to that used in commercial motion picture projection.Alternatively, the effect can also result in confusion or blur perceivedby viewer 30. In practice this confusion is barely noticeable, however,and can be reduced through a higher frame rate or a slower varyingsubject of animation.

[0104] Another possibly useful effect occurs when the image of one frame230 is visible through the slit 220 corresponding to an adjacent frame230. In this case, multiple side-by-side animations may be visible tothe viewer. These “second-order” images can be used for graphic effect,if desired. Or, if not desired, they may be removed by increasingslitboard thickness D_(sb) or the ratio D_(ff)/D_(i), by introducing alight baffle 32 between slitboard 22 and backboard 23, or by alteringthe geometry of backboard 23. All of these techniques are describedbelow.

[0105] Still another possibly useful effect arises from the fact thatthe stretching effect distorts the proportions of image 230. One canremove this effect, if not desired, by preshrinking the images 230 sothat the stretching effect restores the true proportions. Care must betaken, however, in the case where different viewers 30 observe apparatus10, each from a different D_(vs). In this case, the exact restoration toperfect dimensions occurs at one D_(vs) only. At another D_(vs), therestoration is not exact. In practice, however, for many useful rangesof parameters, the improper proportions have few or no adverse effects.

[0106] In general, four parameters are imposed by the environment—V_(w),D_(bs), D_(vs), and D_(i′). V_(w), the viewer's speed, is generallyimposed by, e.g., the speed of the vehicle, typical viewer footspeed, orthe speed of a moving walkway, escalator, etc. D_(bs), thebackboard-to-slitboard distance, is generally limited by the spacebetween a train and the tunnel wall, or the available space of apedestrian walkway, for example. D_(vs), the distance from viewer toslitboard, is imposed by, for example, the width of a subway car or thewidth of a pedestrian walkway. Finally, D_(i′), the perceived imagewidth, should be no larger than the area visible to viewer 30 at a giveninstant—for example, the width of a train window.

[0107] Also generally imposed is the well-established minimum frame ratefor the successful perception of the animation effect—viz.,approximately 15-20 frames per second. The frame rate, theframe-to-frame distance, and viewer speed are related by

Frame rate=V _(w) /D _(ff)  (2)

[0108] Because the frame rate must generally be greater than the minimumthreshold, and V_(w) is generally imposed by the environment, thisrelation sets a maximum D_(ff).

[0109] For example, for a train moving at about 30 miles per hour (about48 kilometers per hour), given a minimum frame rate of about 20 framesper second, the relation above determines that D_(ff) can be as great asabout 2 feet (about 67 cm).

[0110] Alternatively, the minimum V_(w) is determined by the minimumD_(ff) allowable by the image, which is constrained by the fact thatD_(ff) can be no smaller than D_(i). The stretching effect theoreticallyallows D_(i) to be lowered arbitrarily without lowering D_(i′), becauseD_(bs) can, in principle, be lowered arbitrarily. In practice, however,Dbs cannot be lowered arbitrarily, because very small values result invery different perceived image widths for each viewer 30 at a differentD_(vs). That is, at too small a D_(bs), viewers on opposite sides of atrain could see too markedly differently proportioned images. Moreover,small D_(bs), resulting in high magnification, requires correspondinglyhigh image quality or printing resolution.

[0111] If viewers at different distances D_(vs) will observe apparatus10, the closest ones (those with the smallest D_(vs)) generallydetermine the limits on D_(bs).

[0112] Because images cannot overlap,

D_(i)≦D_(ff).  (3)

[0113] If D_(i)=D_(ff) and one can view second order images, they willappear to abut the first order image, slightly out of synchronization.The resulting appearance will be like that of multiple television setsnext to each other and starting their programs at slightly differenttimes. This effect may be used for graphic intent, or, if not desired,three variations in parameters can remove it.

[0114] First, one can decrease the ratio D_(i)/D_(ff), effectivelyputting space between adjacent images. This change will send secondorder images away from the primary ones.

[0115] Second, one may increase slitboard thickness D_(sb) so thatsecond order images are obscured by the cutoff angle. That is, for anynon-zero thickness of slitboard 22, there will be an angle through whichif one looks one will not be able to see through the slits. As thethickness of slitboard 22 increases, this angle gets smaller, and can beseen to follow the relation

D_(sb) /D _(s) ≦D _(bs)/(D _(i)/2)  (4)

[0116] This relation may alternatively be written

D _(sb) /D _(s) ≦D _(vs)/(D _(i′)/2)  (5)

[0117] by substitution for D_(i′) from Relation 1. This shows the limiton D_(sb) imposed by the desired perceived image width.

[0118] The same effect as described in the preceding paragraph can beachieved by placing light baffle 32 between slitboard 22 and backboard23, thereby obstructing the view of one image 230 through the slit 220of an adjacent image 230.

[0119] Third, one can change the shape of the backboard, as illustratedin FIG. 7. In apparatus 70, backboard 71 bears curved images 730 so thatsecond order images are not observed. The change in backboard shape willresult in a slightly altered stretching effect. As before, thisstretching effect can be undone by preshrinking the image in thedirection of motion.

[0120] The embodiment illustrated in FIG. 7 has the potentially usefulproperty not only of showing no second order images, but also of anarbitrarily wide first order image. This effect is related to, butdistinct from, the stretching effect described above, which assumes aflat backboard geometry. The final observed width of the image islimited by the vignetting of the slitboard—the exact relation can befound by solving Relation 5 for D_(i′). It can be observed from FIG. 7that as the viewing angle becomes large, the viewer continues to observethrough each given slit 220 only the image 730 corresponding to thatslit 220. In the ideal limit of zero slitboard width, the leftmostsliver of the image is viewable when the viewer looks 90° to the leftand the rightmost sliver is viewable when the viewer looks 90° to theright. The slivers in between are continuously viewable between theseextreme angles. In other words, each image is observed as infinitelywide. (In FIG. 7, the curved image 730 does not quite reach theslitboard 22, in order to illustrate the maximum viewing angle allowedby the vignetting of a non-zero width slitboard. In principle, the curveof image 730 may reach the slitboard.)

[0121] A further relation is that the slit width must vary inverselywith the light brightness—i.e., D_(s)∝/B. In general, the device hashigher resolution and less blur the smaller the slit width (analogouslyto how a pinhole camera has higher resolution with a smaller pinhole).Since smaller slits transmit less light, the brightness must increasewith decreasing slit width in order that the same total amount of lightreach viewer 30.

[0122] The width of slit 220 relative to the image width determines theamount of blur perceived by viewer 30 in the direction of motion. Morespecifically, the size of slit 220, projected from viewer 30 ontobackboard 23, determines the scale over which the present device doesnot reduce blur. This length is set because the sliver of the image thatcan be seen through slit 220 at any given moment is in motion, andtherefore blurred in the viewer's perception. The size of slit 220relative to the image width should thus be as small as practicable ifthe highest resolution possible is desired. In the parameter ranges ofthe two examples below, slit widths would likely be under about 0.03125inch (under about 0.8 mm).

[0123] The achievable brightness and resolution, and their relationship,can be quantified.

[0124] First, define the following additional parameters:

[0125] L_(ambient)=the ambient luminance of the viewer's environment

[0126] L_(device)=the luminance of the backboard on the apparatus

[0127] c=the contrast between the image and the ambient environment atthe position of the viewer

[0128] D_(vb)=D_(vs)+D_(bs)=the distance between the viewer and thebackboard

[0129] B_(ambient)=the brightness of the ambient environment at theposition of the viewer

[0130] B_(device)=the brightness of the image at the position of theviewer

[0131] TF=the transmission fraction, or fraction of light that passesthrough the slitboard

[0132] R=the image resolution

[0133] L_(ambient) describes the luminance of a typical object withinthe field of view of the viewer while looking at the image projected bythe apparatus. This typical object should be representative of thegeneral brightness of the viewer's environment and should characterizethe background light level. For example, in a subway or train it mightbe the wall of the car adjacent to the window through which theapparatus is viewable.

[0134] B_(ambient) is the brightness of that object as seen by theviewer, and

B _(ambient) =L _(ambient)/4πD_(ambient) ²,  (6)

[0135] where D_(ambient) is the distance between the viewer and theambient object. It is sometimes difficult to select a particular objectas representative of the ambient. As discussed above, in an embodimentused in a subway tunnel, the ambient object could be the wall of thesubway car adjacent the window, in which case D_(ambient) is thedistance from the viewer to the wall. For ease of calculation, this maybe approximated as D_(vs) because the additional distance from thewindow to the apparatus is relatively small.

[0136] L_(device) describes the luminance of the images on the backboardof the apparatus. Because the backboard is always viewed through theslitboard, which effectively filters the light passing through it, itsbrightness at the position of the viewer, B_(device) is

B_(device)=(L_(device)/4πD _(vb) ²)×TF.  (7)

[0137] TF, the transmission fraction of the slitboard, is the ratio ofthe length of slitboard transmitting light to the total length—i.e.,$\begin{matrix}{{{TF} = {{D_{s}/D_{ff}} \leq {( {D_{s} \times D_{vs}} )/( {D_{i}^{\prime} \times D_{bs}} )}}},} & (8)\end{matrix}$

[0138] where equality holds in the second line when D_(ff)=D_(i).

[0139] R, the image resolution, is the ratio of the size of the image tothe size of the slit projected onto the backboard, $\begin{matrix}\begin{matrix}{R = {( {D_{i} \times D_{vs}} )/( {D_{s} \times D_{bs}} )}} \\{\approx {D_{i}/D_{s}}} \\{= {( {D_{i}^{\prime} \times D_{bs}} )/( {D_{s} \times D_{vs}} )}}\end{matrix} & (9)\end{matrix}$

[0140] This quantity is called the resolution because the image tends toblur in the direction of motion on the scale of the width of the slit.Because the eye can see the whole area of the image contained within theslit width at the same time, and the image moves in the time it isvisible, the eye cannot discern detail in the image much finer than theprojected slit width. Therefore D_(s) effectively defines the pixel sizeof the image in the direction of motion. In other words, for example, ifthe slit width is one-tenth the width of the image, the imageeffectively has ten pixels in the direction of motion. In practice, theeye resolves the image to slightly better than R, but R determines thescale.

[0141] In order that the image meaningfully project a non-blurry image,R preferably is greater than 10, but this may depend on the image to beprojected. It should also be noted that R=1/TF when D_(i)=D_(ff), sothat increasing the resolution decreases the transmitted light.

[0142] c is the contrast between the apparatus image and the ambientenvironment at the position of the viewer. In order that the image beviewable in the environment of the viewer, the apparatus brightness mustbe above a minimum brightness

B _(device) ≧B _(ambient) ×c.  (10)

[0143] In order that the device be visible at all, c defines a minimumdevice brightness that depends on the properties of the human eye: ifthe device's image is too dim relative to its environment it will beinvisible. The brightness of the device may always be brighter than theminimum defined by c. Practically speaking, c ought to be at least about0.1. For many applications, such as commercial advertising, it may bedesirable that c be greater than 1.

[0144] The following parameters comprise the smallest set of parameters(which may be referred to as “independent” parameters) that fullydescribe the apparatus according to the invention—D_(vs), D_(bs), V_(w),L_(ambient), D_(ambient), c, L_(device), D_(i), D_(s), and D_(ff). Otherparameters, which may be defined as “dependent parameters” are:

D _(i′) =D _(i) ×D _(vs) /D _(bs)

D _(vb) =D _(vs) +D _(bs)

R=D _(i) /D _(s)

FR=V _(w) /D _(ff)

TF=D _(s) /D _(ff)

B _(ambient) =L _(ambient)/4πD _(ambient) ²

B _(device)=(L _(device)/4πD _(vb) ²)×TF

[0145] Of the independent parameters, the first five are substantiallydetermined by the environment in which the apparatus is installed. In asubway system, for example, these five parameters are determined by thecross sections of the tunnel and train, the train speed, and thelighting in the train. On a pedestrian walkway or building interior, asanother example, these parameters are determined by the dimensions ofthe walkway or hallway, pedestrian foot speed, and the ambient lightingconditions.

[0146] c and the dependent parameters R and FR are constrained byproperties of human perception, and that the image of the apparatus bemeaningful and not overly degraded by blurring. D_(i′) is constrainedeither by the environment (the width of a subway window, for example) orby the requirements of the image to be displayed by the apparatus (suchas aesthetic considerations) or both. The remaining dependent parametersare determined by the independent parameters.

[0147] When these parameters are not substantially constrained, muchgreater leeway is allowed with the remaining four independentparameters, and the specific relationships set forth below need not befollowed. Such relaxed conditions occur, for example, in connection witha surface train traveling outdoors in a flat environment when D_(vs) islargely unconstrained. Sometimes a substantially unconstrained parameterresults in an environment where the apparatus cannot be used at all,such as where the ambient light level varies greatly and randomly or theviewer speed is completely unknown.

[0148] The constraints on the remaining independent parameters are bestexpressed as a series of inequalities and are derived below.

[0149] Combining Relations 6, 7 and 10 provides the minimum slit width,$\begin{matrix}{D_{s} \geq {c \times ( {B_{ambient}/B_{device}} ){( {D_{bs} \times D_{i}^{\prime}} )/D_{vs}}} \geq {c \times ( {L_{ambient}/L_{device}} )( {D_{vb}^{2}/D_{ambient}^{2}} ){( {D_{bs} \times D_{i}^{\prime}} )/D_{vs}}}} & (11)\end{matrix}$

[0150] Solving Relation 9 for D_(s) gives,

D _(s)≦(D _(i′) ×D _(ba))/(R×D _(vs)).  (12)

[0151] Combining Relations 11 and 12 constrains the slit width fromabove and below:

c×(L _(ambient) /L _(device))(D _(vb) ² /D _(ambient) ²)(D _(bs) ×D_(i′))/D _(vs) ≦D _(s)≦(D _(i′) ×D _(bs))/(R×D _(vs)).  (13)

[0152] In this relation, L_(amient) and all the distances except theslit width are substantially constrained by the environment, and R and care constrained by properties of human visual perception. As discussedabove, for ease of calculation, D_(ambient) can be approximated byD_(vs); note also that (D_(bs)×D_(i′))/D_(vs)=D_(i). The inequalitybetween the far left and far right sides of the relation forces aminimum luminance for the apparatus, L_(device). That is, if theluminance of the apparatus is below a minimum threshold, the apparatusimage will be too dim to see in the brightness of the viewer'senvironment.

[0153] Once the luminance of the apparatus is sufficiently high, theinequalities between D_(s) and the far left and far right of therelation determine the allowable slit width range. A smaller slit widthgives higher resolution but less brightness and a greater slit widthgives brightness at the expense of resolution. A higher luminance of theapparatus extends the lower end of the allowable slit width range.

[0154] Another similar relation for the frame-to-frame spacing may bederived from the relations above. Relation 3 may be written$\begin{matrix}{D_{ff} \geq D_{i} \geq {( {D_{i}^{\prime} \times D_{bs}} )/{D_{vs}.}}} & (14)\end{matrix}$

[0155] Relation 2, frame rate=V_(w)/D_(ff), may be rewritten

D _(ff) ≦V _(w) /FR,  (15)

[0156] where FR denotes the frame rate and the equality has changed toan inequality to reflect that FR is a minimum frame rate necessary forthe animation effect to work.

[0157] Combining Relations 14 and 15 yields,

(D _(i′) ×D _(bs))/D _(vs) ≦D _(ff) ≦V _(w) /FR.  (16)

[0158] V_(w) and all the distances except D_(ff) are substantiallyconstrained by the environment, and FR is constrained by properties ofhuman visual perception. Therefore the relation defines an allowablerange for D_(ff). It also puts a condition on the environments in whichthe present invention may be applied—i.e., if the inequality does nothold between the far left and far right hand sides of the relation, thepresent invention will not be useful.

[0159] Choosing a lower D_(ff) puts second order frames closer to firstorder frames while improving the frame rate. Decreasing D_(ff) alsoincreases the transmission fraction without decreasing the resolution.Choosing a higher D_(ff) moves the images farther apart at the expenseof a reduced frame rate.

[0160] Though in principle apparatus 10 requires no included lightsource for its operation if ambient light is sufficient, such asoutdoors (lid 21 or backboard 23 would have to be light-transmissive),in practice the use of very thin slits does impose such a requirement.That is, when operated under conditions of low ambient light anddesiring moderate resolution, bright interior illumination ispreferable. The designation “interior” indicates the volume of theapparatus 10 between backboard 23 and slitboard 22, as opposed to the“exterior,” which is every place else. The interior will contain theviewable images 230, but otherwise may be empty or contain supportstructure, illumination sources, optical baffles, etc. as describedabove in connection with FIGS. 1, 2 and 2A.

[0161] Moreover, this illumination preferably should not illuminate theexterior of the device, or illuminate the viewer's environment or reachthe viewer directly, because greater contrast between the dark exteriorand bright interior improves the appearance of the final image. Thislighting requirement is less cumbersome than that for stroboscopicdevices—in a subway tunnel environment, this illumination need not bebrighter than achievable with ordinary residential/commercial typelighting, such as fluorescent tubes. The lighting preferably should beconstant, so no timing complications arise. Preferably the interior ofapparatus 10 should be physically sealed as well as possible from theexterior subway tunnel environment as discussed above, preferably whilepermitting dissipation of heat from the light source, if necessary. Theenclosure may also be used to aid the illumination of the interior byreflecting light which would otherwise not be directed towards viewableimages 230.

[0162] Two examples show in more detail how the various parametersinterrelate.

Example 1

[0163] The first example illustrates how all constraints tend to relaxas V_(w) increases. For example, in a typical subway system thefollowing parameters may be imposed:

[0164] V_(w)≈30 mph (train speed)

[0165] D_(bs)≈6 inches (space between train and wall)

[0166] D_(vo)≈6 feet (half the width of a train, for the averagelocation of a viewer 30 within the car)

[0167] D_(i′)≈3 feet (width of train window) By Relations (3) and (1),$\begin{matrix}{D_{ff} \geq D_{i} \geq {( {D_{i}^{\prime} \times D_{bs}} )/D_{vs}} \geq {( {3\quad {ft} \times 0.5\quad {ft}} )\text{/}6\quad {ft}} \geq {0.25\quad {{feet}.}}} & (17)\end{matrix}$

[0168] If the images are abutted so that D_(ff)=D_(i), the maximum framerate is attained. Then, by Relation (2), $\begin{matrix}\begin{matrix}{{{Frame}\quad {rate}} = {30\quad {mph}\text{/}0.25\quad {ft}}} \\{= {176\quad {frames}\quad {per}\quad {{second}.}}}\end{matrix} & (18)\end{matrix}$

[0169] At this rate the parameters can be adjusted a great deal whilestill maintaining high quality animation. This frame rate is also highenough to support interlacing of images (see above) if desired, despitethe reduction in effective frame rate that results from interlacing.

Example 2

[0170] The second example illustrates how the constraints tighten whennear the minimal frame rate. To find the lowest practicable V_(w),assume the following parameters:

[0171] frame rate≈20 frames/sec

[0172] D_(bs)≈6 inch

[0173] D_(vs)≈6 feet

[0174] D_(i′)≈2 feet.

[0175] By Relation (1), $\begin{matrix}{D_{i} = {( {D_{bs} \times D_{i}^{\prime}} )/D_{vs}}} \\{= {{( {0.5\quad {ft} \times 2\quad {ft}} )/6}\quad {ft}}} \\{= {2\quad {{inches}.}}}\end{matrix}$

[0176] For abutted images, D_(ff)=D_(i), and, $\begin{matrix}{V_{w} = {D_{ff} \times {frame}\quad {rate}}} \\{= {2\quad {inches} \times 20\quad {frames}\text{/}\sec}} \\{{= {40\quad {inches}\text{/}\sec}},}\end{matrix}$

[0177] which is approximately pedestrian footspeed.

[0178] The implication of this last result—that the device cansuccessfully display quality animations to pedestrian traffic—vastlyincreases the potential applicability of this device relative tostroboscopically based arrangements.

[0179] The following alternative preferred embodiments are within thespirit and scope of the invention.

[0180]FIG. 8 illustrates another preferred embodiment 80 altering theoptimal viewing angle of the animation. In apparatus 80, backboard 83bears images 830 that are inclined at an acute angle to backboard 83,varying the viewing angle from a right angle to that acute angle. Thisalteration permits more natural viewing for a pedestrian, for example,by not requiring turning of the pedestrian's head far away from thedirection of motion. This embodiment may also eliminate second orderimages.

[0181]FIG. 9 illustrates a further preferred embodiment 90 similar toapparatus 80, but in which slitboard 92 is also angled. This refinementagain provides a more natural viewing position for a pedestrian. Theasymmetric triangular design permits natural viewing for viewers movingfrom left to right. A symmetric design (not shown), in which the plan ofthe slitboard might more resemble, for example, a series of isoscelestriangles, could accommodate viewers moving in both directions.

[0182]FIG. 10 illustrates a technique of using one slitboard 101 as thebackboard of a different slitboard 102, while simultaneously using thatslitboard 102 as the backboard of the original slitboard 101. Thisconfiguration permits the back-to-back installation of two devices inthe space of one. This apparatus 100 may be improved by offsetting oneset of slits from the other by D_(i)/2, or some fraction of D_(i).

[0183]FIG. 11 shows a simple schematic plan view of apparatus 100. Slits220 of one slitboard 101 are centered between slits 220 of the oppositeslitboard 102, which is acting as the former slitboard's backboard. Thatis, between slits 220 of one slitboard are images 230 viewable throughthe other slitboard, and vice-versa. Because the slits are very thin,their presence in the backboard creates negligible distraction.

[0184]FIG. 12 shows another embodiment 120 similar to apparatus 100, buthaving a set of curved images 1230 (as in FIG. 7) facing slits 220 ofopposite slitboards/backboards 101, 102. Apparatus 120 thus hascharacteristics, and advantages, of both apparatus 70 and apparatus 100.

[0185]FIG. 13 illustrates a roller type of image display mechanism 130that may be placed at the position of the backboard. The rollers maycontain a plurality of sets of images that can be changed by simplyrolling from one set of images to another. Such a mechanism allows thechanging of images to be greatly simplified. In order to change from oneanimation to another, instead of manually changing each image, one mayroll such rollers to a different set of images. This change could beperformed manually or automatically, for instance by a timer. Byincorporating slits 220, mechanism 130 can be used in apparatus 100 orapparatus 120.

[0186] Yet another preferred embodiment 140 is shown in FIGS. 14 and 15.In apparatus 140, “backboard” 141, with its images 142, is placedbetween viewer 30 and a series of mirrors 143. Each mirror 143preferably is substantially the same size and orientation as any slitsthat would have been used in the aforementioned embodiments. Mirrors 143preferably are mounted on a board 144 that takes the place of theslitboard, but mirrors 143 could be mounted individually or on any othersuitable mounting. The principles of operation of apparatus 140 aresubstantially the same as those for the aforementioned embodiments.However, because “backboard” 141 would obscure the sight of mirrors 143by viewer 30, “backboard” 141 may be placed above or below the line ofsight of viewer 30. As shown in FIGS. 14 and 15, “backboard” 141 isabove the line of sight of viewer 30. As drawn in FIGS. 14 and 15,moreover, both “backboard” 141 and “mirrorboard” 144 are inclined.However, with proper placement, inclination of boards 141, 144 may notbe necessary. As in the case of a slitboard, “mirrorboard” 144 will workbest when its non-mirror portions are dark, to increase the contrastwith the images.

[0187] A complete animation displayed using the apparatus of the presentinvention for use in a subway system may be a sizable fraction of a mile(or more) in length. In accordance with another aspect of the invention,such an animation can be implemented by breaking the backboard carryingthe images for such an animation into smaller units, providing multipleapparatus according to the invention to match the local design of thesubway tunnel structure where feasible. Many subway systems haverepeating support structure along the length of a tunnel to which suchmodular devices may be attached in a mechanically simplified way.

[0188] As an example, the New York City subway system has throughout itstunnel network regularly spaced columns of support I-beams between manypairs of tracks. Installation of apparatus according to the presentinvention may be greatly facilitated by taking advantage of theseI-beams, their regular spacing, and the certainty of their placementjust alongside, but out of, the path of the trains. However, this singleexample should not be construed as restricting the applicability to justone subway system.

[0189] The modularization technique has many other advantages. It hasthe potential to facilitate construction and maintenance, by takingadvantage of structures explicitly designed with the engineering of thesubway tunnels in mind. The I-beam structure is sturdy and guaranteednot to encroach on track space. The constant size of the I-beamsconsistently regulates D_(bs), easing design considerations.Additionally, cost and engineering difficulties are reduced insofar asthe apparatus may be easily attached to the exterior of the supportswithout drilling or possibly destructive alterations to existingstructure.

[0190]FIG. 16 schematically illustrates an example of the modularizationpossible for the two-sided apparatus of FIGS. 10 and 11. As shown,construction of the whole length of two slitboards, which could be ahalf mile or more in length, is reduced to constructing many identicalslitboards 160, each about as long as the distance between adjacentI-beam columns 161 (e.g., about five feet). Each of the slitboards isthen attached to a pair of the existing support I-beams, along with theother parts of the apparatus as described above.

[0191] Thus it is seen that display devices for use inspatially-constrained environments that display still images appearinganimated to viewers in motion are provided. One skilled in the art willappreciate that the present invention can be practiced by other than thedescribed embodiments, which are presented for purposes of illustrationand not of limitation, and the present invention is limited only by theclaims which follow.

1. Apparatus for displaying a plurality of still images, forming ananimated display, to a viewer moving substantially at a known velocityrelative to said still images substantially along a known trajectorysubstantially parallel to said still images, said apparatus comprising:a backboard having a backboard length along said trajectory, said stillimages being mounted on a surface of said backboard, each of said stillimages having an actual image width and having an image center; and aslitboard positioned substantially parallel to said backboard, facingsaid surface thereof and separated therefrom by a board-to-boarddistance, said slitboard being mounted at a viewing distance from saidtrajectory, said board-to-board distance and said viewing distancetotaling a backboard distance, said slitboard having a slitboard lengthalong said trajectory, and having a plurality of slits substantiallyperpendicular to said slitboard length, each said slit corresponding toat least one of said images and having a slit width measured along saidslitboard length and a slit center, respective slit centers of adjacentones of said slits being separated by a frame-to-frame distance;wherein: in order to project each said image substantially withoutblurring, said slit width is selected to be at most about one-tenth ofsaid actual image width; said images are illuminated to an imageluminance; and when said viewer is in an environment illuminated to anambient luminance, said slit width is at least about equal to one-tenththe product of (a) said actual image width, (b) the square of thequotient of said backboard distance and said viewing distance, and (c)the quotient of said ambient luminance and said image luminance.
 2. Theapparatus of claim 1 further comprising an enclosure for preventingentry of foreign matter between said slitboard and said backboard. 3.The apparatus of claim 1 further comprising a light source forilluminating said images to said image luminance.
 4. The apparatus ofclaim 3 wherein said light source is between said slitboard and saidbackboard.
 5. The apparatus of claim 3 wherein: said backboard islight-transmissive; and said backboard is between said light source andsaid slitboard.
 6. Apparatus for displaying a plurality of still images,forming an animated display, to a viewer moving substantially at a knownvelocity relative to said still images substantially along a knowntrajectory substantially parallel to said still images, said apparatuscomprising: a backboard having a backboard length along said trajectory,said still images being mounted on a surface of said backboard, each ofsaid still images having an actual image width and having an imagecenter; a slitboard positioned substantially parallel to said backboard,facing said surface thereof and separated therefrom by a board-to-boarddistance, said slitboard being mounted at a viewing distance from saidtrajectory, said board-to-board distance and said viewing distancetotaling a backboard distance, said slitboard having a slitboard lengthalong said trajectory, and having a plurality of slits substantiallyperpendicular to said slitboard length, each said slit corresponding toat least one of said images and having a slit width measured along saidslitboard length and a slit center, respective slit centers of adjacentones of said slits being separated by a frame-to-frame distance; and asubstantially cylindrical lens in each said slit; wherein: in order toproject each said image substantially without blurring, said slit widthis selected to be at most about one-tenth of said actual image width. 7.The apparatus of claim 6 further comprising a light source forilluminating said images.
 8. Apparatus for displaying a plurality ofstill images, forming an animated display, to a viewer movingsubstantially at a known velocity relative to said still imagessubstantially along a known trajectory substantially parallel to saidstill images, said apparatus comprising: a backboard having a backboardlength along said trajectory, said still images being mounted on asurface of said backboard, each of said still images having an actualimage width and having an image center; and a slitboard positionedsubstantially parallel to said backboard, facing said surface thereofand separated therefrom by a board-to-board distance, said slitboardbeing mounted at a viewing distance from said trajectory, saidboard-to-board distance and said viewing distance totaling a backboarddistance, said slitboard having a slitboard length along saidtrajectory, and having a plurality of slits substantially perpendicularto said slitboard length, each said slit corresponding to at least oneof said images and having a slit width measured along said slitboardlength and a slit center, respective slit centers of adjacent ones ofsaid slits being separated by a frame-to-frame distance; wherein: inorder to project each said image substantially without blurring, saidslit width is selected to be at most about one-tenth of said actualimage width; and said trajectory, said backboard and said slitboard arecurved.
 9. The apparatus of claim 8 further comprising a light sourcefor illuminating said images.
 10. The apparatus of claim 8 furthercomprising an enclosure for preventing entry of foreign matter betweensaid slitboard and said backboard.
 11. Apparatus for displaying aplurality of still images, forming an animated display, to a viewermoving substantially at a known velocity relative to said still imagessubstantially along a known trajectory substantially parallel to saidstill images, said apparatus comprising: a backboard having a backboardlength along said trajectory, said still images being mounted on asurface of said backboard, each of said still images having an actualimage width and having an image center; a slitboard positionedsubstantially parallel to said backboard, facing said surface thereofand separated therefrom by a board-to-board distance, said slitboardbeing mounted at a viewing distance from said trajectory, saidboard-to-board distance and said viewing distance totaling a backboarddistance, said slitboard having a slitboard length along saidtrajectory, and having a plurality of slits substantially perpendicularto said slitboard length, each said slit corresponding to at least oneof said images and having a slit width measured along said slitboardlength and a slit center, respective slit centers of adjacent ones ofsaid slits being separated by a frame-to-frame distance; and anenclosure for preventing entry of foreign matter between said slitboardand said backboard; wherein: in order to project each said imagesubstantially without blurring, said slit width is selected to be atmost about one-tenth of said actual image width.
 12. The apparatus ofclaim 11 wherein said slitboard and said backboard form portions of saidenclosure.
 13. The apparatus of claim 11 further comprising a respectivetransparent covering for each said slit.
 14. The apparatus of claim 11further comprising a light source for illuminating said images.
 15. Theapparatus of claim 11 wherein said known trajectory is a subway track,said viewer being a passenger on a subway train traveling on said subwaytrack.
 16. Apparatus for displaying a plurality of still images, formingan animated display, to a viewer moving substantially at a knownvelocity relative to said still images substantially along a knowntrajectory substantially parallel to said still images, said apparatuscomprising: a backboard having a backboard length along said trajectory,said still images being mounted on a surface of said backboard, each ofsaid still images having an actual image width and having an imagecenter; and a slitboard positioned substantially parallel to saidbackboard, facing said surface thereof and separated therefrom by aboard-to-board distance, said slitboard being mounted at a viewingdistance from said trajectory, said board-to-board distance and saidviewing distance totaling a backboard distance, said slitboard having aslitboard length along said trajectory, and having a plurality of slitssubstantially perpendicular to said slitboard length, each said slitcorresponding to at least one of said images and having a slit widthmeasured along said slitboard length and a slit center, respective slitcenters of adjacent ones of said slits being separated by aframe-to-frame distance; wherein: in order to project each said imagesubstantially without blurring, said slit width is selected to be atmost about one-tenth of said actual image width; and said frame-to-framedistance is selected with regard to said known velocity to produce adesired frame rate to be seen by said viewer, said frame rate being atleast about 15 frames per second.
 17. The apparatus of claim 16 whereinsaid known trajectory is a subway track, said viewer being a passengeron a subway train traveling on said subway track.
 18. The apparatus ofclaim 16 wherein said known trajectory is a walkway, said viewer being apedestrian on said walkway.
 19. The apparatus of claim 16 wherein saidimages are curved relative to said backboard and said slitboard.
 20. Theapparatus of claim 16 wherein said images are inclined relative to saidbackboard and said slitboard.
 21. The apparatus of claim 16 furthercomprising a light source for illuminating said images.
 22. Theapparatus of claim 16 further comprising an enclosure for preventingentry of foreign matter between said slitboard and said backboard. 23.Apparatus for displaying a plurality of still images, forming ananimated display, to a viewer moving substantially at a known velocityrelative to said still images substantially along a known trajectorysubstantially parallel to said still images, said apparatus comprising:a backboard having a backboard length along said trajectory, said stillimages being mounted on a surface of said backboard, each of said stillimages having an actual image width and having an image center; and aslitboard positioned substantially parallel to said backboard, facingsaid surface thereof and separated therefrom by a board-to-boarddistance, said slitboard being mounted at a viewing distance from saidtrajectory, said board-to-board distance and said viewing distancetotaling a backboard distance, said slitboard having a slitboard lengthalong said trajectory, and having a plurality of slits substantiallyperpendicular to said slitboard length, each said slit corresponding toat least one of said images and having a slit width measured along saidslitboard length and a slit center, respective slit centers of adjacentones of said slits being separated by a frame-to-frame distance;wherein: in order to project each said image substantially withoutblurring, said slit width is selected to be at most about one-tenth ofsaid actual image width; and each of said slit centers is directlyopposite a respective one of said image centers.
 24. Apparatus fordisplaying a plurality of still images, forming an animated display, toa viewer moving substantially at a known velocity relative to said stillimages substantially along a known trajectory substantially parallel tosaid still images, said apparatus comprising: a backboard having abackboard length along said trajectory, said still images being mountedon a surface of said backboard, each of said still images having anactual image width and having an image center; and an opticalarrangement positioned to transmit light from said images to said vieweralong said trajectory, said optical arrangement having optical elementsviewed by said viewer at a viewing distance from said trajectory, eachrespective one of said optical elements being at an optical distancefrom a respective one of said images and having an element widthmeasured parallel to said trajectory and an element center along saidwidth, respective element centers of adjacent ones of said elementsbeing separated by a frame-to-frame distance; wherein: in order toproject each said image substantially without blurring, said elementwidth is selected to be at most about one-tenth of said actual imagewidth; said images are illuminated to an image luminance; and when saidviewer is in an environment illuminated to an ambient luminance, saidelement width is at least about equal to one-tenth the product of (a)said actual image width, (b) the square of the quotient of (i) the sumof said viewing distance and said optical distance and (ii) said viewingdistance, and (c) the quotient of said ambient luminance and said imageluminance.
 25. The apparatus of claim 24 wherein at least one of saidoptical elements is a mirror.